OK, that's not great, but not the worst I've seen by a long shot.
The pic with the solder on it I can see 2 shorts that caused all kind of problems, as well as a couple of missing components that are/were most likely the direct cause of the Headset issue.
The pic with all of the solder removed isn't bad looking, aside from the missing pads and components L1 and L4.
Since there is no pic of the board before you laid the iron to her I can't say if repairing these issues will get it up and going again.
You can look at the first pic I posted, or the one that you numbered, as that's the same CL version you're working on there to see the missing components. L1 and L4 are inductors, and you can probably get away with just using a jumper wire in their place here, but that's not always the case. At a minimum you'll need to replace/rewire L4 and install a jumper wire to try and close that switch so the controller will think no headset is plugged in there.
I recommend using 30awg wire for this and a little practice on something else before sticking the iron back on there as it looks like you're leaving the thing on there far too long, it only takes a second or two at most to make a solid joint on these kind of smaller spots with new solder.
This is just a quick diagram of what you can try to get the Heasdet switch working, not the entire headset, just so a Wireless one will work again for now.
Use 30awg wire and strip off the insulation and use it to connect the Blue spots, since that's a short run there's no point in having the insulation or making some kind of loop with a longer piece of wire. Doing it this way will not replace L4, but jumper it as well as restore the connection to that pin in one shot.
For the pink spots, they can just be connected with a short piece of 30awg wire.
Again, these will only restore the switch function that the Headset connector provides, and if this is done properly, and there are no other issues with the controller, then a Wireless headset should start working again with the controller.